Method and system of determining in-plane motion in propeller data

ABSTRACT

The present invention is directed to a method of MR imaging whereby a k-space blade extending through a center of k-space from a subject in motion is acquired. A high-pass convolution of the k-space blade with a reference k-space blade is then determined and converted to a δ function. In-plane motion of the subject during data acquisition of the k-space is then determined from the δ function.

CROSS REFERENCE TO RELATED APPLICATIONS

The present application is a continuation of and claims priority of U.S.Ser. No. 11/170,054 filed on Jun. 29, 2005, the disclosure of which isincorporated herein by reference.

BACKGROUND OF THE INVENTION

The present invention relates generally to magnetic resonance (MR)imaging and, more particularly, to a method and system of determiningin-plane motion of a subject from which MR data is acquired in aPeriodically Rotated Overlapping Parallel Lines with EnhancedReconstruction (PROPELLER) acquisition, or variant thereof.

When a substance such as human tissue is subjected to a uniform magneticfield (polarizing field B₀), the individual magnetic moments of thespins in the tissue attempt to align with this polarizing field, butprecess about it in random order at their characteristic Larmorfrequency. If the substance, or tissue, is subjected to a magnetic field(excitation field B₁) which is in the x-y plane and which is near theLarmor frequency, the net aligned moment, or “longitudinalmagnetization”, M_(z), may be rotated, or “tipped”, into the x-y planeto produce a net transverse magnetic moment M_(t). A signal is emittedby the excited spins after the excitation signal B₁ is terminated andthis signal may be received and processed to form an image.

When utilizing these signals to produce images, magnetic field gradients(G_(x), G_(y), and G_(z)) are employed. Typically, the region to beimaged is scanned by a sequence of measurement cycles in which thesegradients vary according to the particular localization method beingused. The resulting set of received NMR signals are digitized andprocessed to reconstruct the image using one of many well knownreconstruction techniques.

Fast Spin Echo (FSE) imaging is an imaging technique commonly used as anefficient method of collecting MRI data with minimal artifact.Generally, FSE requires that the refocusing B₁ pulses be applied betweeneach echo such that their phase is substantially identical to that ofthe initial spin phase after excitation, commonly referred to as the“CPMG” condition. If this condition is not met, the resulting MR signalis generally highly sensitive to the strength of B₁, and therefore willgenerally decay rapidly in successive echoes.

FSE imaging is an imaging technique that has been implemented with anumber of pulse sequence designs. For example, PROPELLER is an FSEtechnique that encodes an MR signal by collecting data during an echotrain such that a rectangular strip, or “blade”, through the center ofk-space is measured. This strip is incrementally rotated in k-spaceabout the origin in subsequent echo trains, thereby allowing adequatemeasurement of the necessary regions of k-space for a desiredresolution. PROPELLER is particularly effective at reducing the effectsof patient motion during data acquisition. Accordingly, PROPELLER isparticularly useful for imaging patients, such as children, who tend tomove or tremor during data acquisition.

In conventional PROPELLER scans, redundant low-frequency k-space datafrom overlapping blades is compared to one another to determine in-planemotion of the patient between acquisition of the k-space blades. In thisregard, the low-frequency k-space data is “gridded” from a Cartesianlattice to a polar lattice to estimate the patient's in-plane motionrelative to a k-space reference blade or image. As such, in-plane motionin a given k-space blade is estimated by computing the convolution ofthe given k-space blade with a k-space reference blade. Nevertheless,while reasonably effective, the convolution is extremely smooth whichmakes identification of the maximum point in the convolution difficultto identify. The maximum point corresponds to the patient's positionduring acquisition of the given k-space blade relative to the k-spacereference blade or image and is used to determine appropriate parametersof a motion correction algorithm. Accordingly, there is a need to makethe maximum point of the convolution more conspicuous and, thus, easierto identify.

It would therefore be desirable to have a system and method forevaluating MR data, acquired with PROPELLER or a variant thereof, todetermine in-plane motion of a subject during data acquisition that moresignificantly identifies a maximum peak of the convolution of a k-spaceblade with a k-space reference blade.

BRIEF DESCRIPTION OF THE INVENTION

The present invention provides a system and method of determiningin-plane motion in MR data that overcomes the aforementioned drawbacks.Low frequency k-space data is processed and evaluated to effectivelydetermine subject motion during the acquisition of the k-space data. Inone embodiment, the convolution of a given k-space blade with a k-spacereference blade is converted to a δ function with a well-defined peakthat corresponds to the maximum point in the convolution. The relativeposition of this well-defined peak is used to determine subject motionduring acquisition of the given k-space blade relative to the k-spacereference blade. This present invention is particularly applicable forMR data acquired using PROPELLER, variants thereof, such as split-bladePROPELLER and TURBOPROP, as well as equivalents thereof.

Therefore, in accordance with one aspect of the invention, an MR systemincludes a plurality of gradient coils positioned about a bore of amagnet to impress a polarizing magnetic field. An RF transceiver systemand an RF switch are controlled by a pulse module to transmit andreceive RF signals to and from an RF coil assembly to acquire MR images.The MR system also includes a computer programmed to acquire a pluralityof k-space blades from a subject in motion during data acquisition, eachk-space blade rotated about a center of k-space. The computer is furtherprogrammed to determine a k-space reference blade and determine ahigh-pass convolution of a k-space blade with the reference k-spaceblade. The computer then determines, from the high-pass convolution,motion of the subject during acquisition of the k-space blade relativeto the k-space reference blade.

In accordance with another aspect of the present invention, the MRsystem includes a plurality of gradient coils positioned about a bore ofa magnet to impress a polarizing magnetic field and an RF transceiversystem and an RF switch controlled by a pulse module to transmit RFsignals to an RF coil assembly to acquire MR images. The system furtherhas a computer programmed to acquire a plurality of k-space blades froma subject in motion during data acquisition, each k-space blade rotatedabout a center of k-space. The computer is further programmed todetermine a k-space reference blade image and convert k-space data froma given k-space blade as well as a k-space reference blade to a commonpolar lattice. The computer is further programmed to Fourier transformthe given k-space blade and the k-space referenced blade and determine ahigh-pass convolution of the Fourier transforms with respect to polarangle of the k-space reference blade and the given k-space blade. Fromthe high-pass convolution, the computer is further programmed todetermine in-plane rotation of the subject during acquisition of thek-space blade relative to the k-space reference blade.

According to another aspect, the present invention is directed to amethod of MR imaging whereby a k-space blade extending through a centerof k-space from a subject in motion is acquired. A high-pass convolutionof the k-space blade with a reference k-space blade is designed so thatthe result is a δ function. In-plane motion of the subject during dataacquisition of the k-space is then determined from the δ function.

In accordance with another aspect, the invention is embodied in acomputer program stored on a computer readable storage medium and havinginstructions which, when executed by a computer, cause the computer toacquire a k-space blade extending through an origin of k-space from asubject in motion during data acquisition. The computer is furthercaused to represent the k-space blade on a polar lattice and determine aconvolution of the k-space blade with a reference k-space blade. Thecomputer is further programmed to high-pass filter the convolution anddetermine at least one of a rotational or a transitional shift of thesubject during acquisition of the k-space blade relative to thereference k-space blade.

Various other features and advantages of the present invention will bemade apparent from the following detailed description and the drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

The drawings illustrate one preferred embodiment presently contemplatedfor carrying out the invention.

In the drawings:

FIG. 1 is a schematic block diagram of an MR imaging system for use withthe present invention.

FIG. 2 is a diagram of a portion of a PROPELLER pulse sequence.

FIG. 3 illustrates a k-space blade acquired with the pulse sequenceillustrated in FIG. 2.

FIG. 4 is a graphical illustration of the convolution of a blade imagewith a reference blade image.

FIG. 5 is a graphical illustration of the k-space blade of FIG. 3arranged on a Cartesian lattice.

FIG. 6 is a graphical illustration of the k-space blade illustrated inFIG. 5 arranged on a polar lattice.

FIG. 7 is a graphical illustration of an approximate δ functiongenerated from the convolution of the image of the k-space blade's phasewith the image of a k-space reference blade's phase.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

The present invention is directed to a method and system of determiningin-plane motion of a subject during data acquisition with a PROPELLER,PROPELLER-variant, or equivalent protocol.

Referring now to FIG. 1, the major components of a preferred magneticresonance imaging (MRI) system 10 incorporating the present inventionare shown. The operation of the system is controlled from an operatorconsole 12 which includes a keyboard or other input device 13, a controlpanel 14, and a display screen 16. The console 12 communicates through alink 18 with a separate computer system 20 that enables an operator tocontrol the production and display of images on the display screen 16.The computer system 20 includes a number of modules which communicatewith each other through a backplane 20 a. These include an imageprocessor module 22, a CPU module 24 and a memory module 26, known inthe art as a frame buffer for storing image data arrays. The computersystem 20 is linked to disk storage 28 and tape drive 30 for storage ofimage data and programs, and communicates with a separate system control32 through a high speed serial link 34. The input device 13 can includea mouse, joystick, keyboard, track ball, touch activated screen, lightwand, voice control, or any similar or equivalent input device, and maybe used for interactive geometry prescription.

The system control 32 includes a set of modules connected together by abackplane 32 a. These include a CPU module 36 and a pulse generatormodule 38 which connects to the operator console 12 through a seriallink 40. It is through link 40 that the system control 32 receivescommands from the operator to indicate the scan sequence that is to beperformed. The pulse generator module 38 operates the system componentsto carry out the desired scan sequence and produces data which indicatesthe timing, strength and shape of the RF pulses produced, and the timingand length of the data acquisition window. The pulse generator module 38connects to a set of gradient amplifiers 42, to indicate the timing andshape of the gradient pulses that are produced during the scan. Thepulse generator module 38 can also receive patient data from aphysiological acquisition controller 44 that receives signals from anumber of different sensors connected to the patient, such as ECGsignals from electrodes attached to the patient. Finally, the pulsegenerator module 38 connects to a scan room interface circuit 46 whichreceives signals from various sensors associated with the condition ofthe patient and the magnet system. It is also through the scan roominterface circuit 46 that a patient positioning system 48 receivescommands to move the patient to the desired position for the scan.

The gradient waveforms produced by the pulse generator module 38 areapplied to the gradient amplifier system 42 having Gx, Gy, and Gzamplifiers. Each gradient amplifier excites a corresponding physicalgradient coil in a gradient coil assembly generally designated 50 toproduce the magnetic field gradients used for spatially encodingacquired signals. The gradient coil assembly 50 forms part of a magnetassembly 52 which includes a polarizing magnet 54 and a whole-body RFcoil 56. A transceiver module 58 in the system control 32 producespulses which are amplified by an RF amplifier 60 and coupled to the RFcoil 56 by a transmit/receive switch 62. The resulting signals emittedby the excited nuclei in the patient may be sensed by the same RF coil56 and coupled through the transmit/receive switch 62 to a preamplifier64. The amplified MR signals are demodulated, filtered, and digitized inthe receiver section of the transceiver 58. The transmit/receive switch62 is controlled by a signal from the pulse generator module 38 toelectrically connect the RF amplifier 60 to the coil 56 during thetransmit mode and to connect the preamplifier 64 to the coil 56 duringthe receive mode. The transmit/receive switch 62 can also enable aseparate RF coil (for example, a surface coil) to be used in either thetransmit or receive mode.

The MR signals picked up by the RF coil 56 are digitized by thetransceiver module 58 and transferred to a memory module 66 in thesystem control 32. A scan is complete when an array of raw k-space datahas been acquired in the memory module 66. This raw k-space data isrearranged into separate k-space data arrays for each image to bereconstructed, and each of these is input to an array processor 68 whichoperates to Fourier transform the data into an array of image data. Thisimage data is conveyed through the serial link 34 to the computer system20 where it is stored in memory, such as disk storage 28. In response tocommands received from the operator console 12, this image data may bearchived in long term storage, such as on the tape drive 30, or it maybe further processed by the image processor 22 and conveyed to theoperator console 12 and presented on the display 16.

The present invention is directed to a variable-density multi-shotacquisition of MR data from a subject in motion during data acquisitionusing the MR system of FIG. 1, or equivalents thereof. This motion isgenerally the product of subject discomfort during the MR scan and isparticularly prevalent in the imaging of children and those anxiousabout being placed in the bore of the magnet. In one embodiment, aPROPELLER acquisition, which can be either a fast spin echo (FSE) or“gradient and spin echo” (GRASE) imaging technique acquires MR data bycollecting a rectangular strip, or “blade”, of k-space during an echotrain. With a PROPELLER acquisition, this strip is incrementally rotatedin k-space about the k-space origin in subsequent repetition time (TR),thereby allowing adequate measurement of the necessary regions ofk-space for a desired resolution and field-of-view. The spin echoes inthe PROPELLER sequence mitigate T2* decay and susceptibility artifacts.Over-sampling the central region of k-space also reduces artifactscaused by subject motion and, thus, improves image quality.

Referring now with particularity to a PROPELLER based acquisition, sinceeach blade or k-space segment extends through the center or centralregion of k-space, the PROPELLER acquisition provides a variable-densitysampling of k-space. More particularly, the “blade” of k-space isrotated about the center of k-space with each subsequent TR of the pulsesequence. As such, with subsequent TRs, the blade, which extends throughthe central region of k-space, is rotated to sample the remainingportions of k-space while resampling the central region of k-space.

Referring now to FIG. 2, a portion of a pulse sequence 70 to acquire MRdata in accordance with a PROPELLER protocol is shown. It should benoted that the phase encoding pulses, balancing gradients, and gradientcrushers are not shown. The pulse sequence 70, in the illustratedexample, is designed to acquire 12 spin-echoes 72 from a region ofinterest. The spin-echoes are all collected relative to a single axis,e.g. G_(x). In this regard, the 12 spin-echoes include odd spin-echoesas well as even spin-echoes. Each spin-echo 72 is acquired following anRF refocusing pulse 74 and during a frequency encoding pulse 76, aseries of which are played out during steady-state conditions. The spinecho data is used to fill k-space which is schematically represented inFIG. 3.

FIG. 3 illustrates schematically a k-space 78 to be filled with MR datain accordance with one contemplated k-space filling scheme. WithPROPELLER, each echo sampled corresponds to a single line 80 of k-space78. As such, for a 12 spin-echo data acquisition, each blade 82 ofk-space includes 12 lines of data. In the illustrated example, eachdashed line 84 represents an odd spin-echo trajectory and the solidlines 86 represent the even spin-echo trajectories. As shown, the evenspin-echoes 86 are placed in a center of the k-space blade 82 and theodd spin-echoes 84 are placed about a periphery of the even spin-echolines 86. It is understood that the present invention is not limited tok-space blades having the orientation between odd and even echoesillustrated in FIG. 3.

As described, PROPELLER-based imaging implements a rotation of theblades of k-space data with each echo-train. In this regard, the bladeof k-space will be incrementally rotated about the center 88 of k-spacewith each echo-train acquisition until k-space is filled. When thek-space is filled, the MR data will be processed for motion correctionand other post-acquisition processes. After these corrections, estimatesof patient motion are taken into account during final imagereconstruction.

PROPELLER MR data is generally processed to estimate subject motionbefore image reconstruction. One known approach to determining subjectmotion during acquisition of a k-space blade is to evaluate theconvolution of the blade image with a reference blade image. Thisconvolution is evaluated via FFT, by first Fourier upsampling and thenzero padding each k-space blade. Fourier upsampling k-space blades by afactor of 2 serves to double the FOV of the convolution, avoidingwrap-around. Zero-padding the k-space blades increases resolution of theconvolution, making subsequent detection of the peak magnitude easier.Absent random noise, the maximum magnitude value of the convolution ispositioned at the point corresponding to the shift, x_(shift), of thek-space blade relative to the k-space reference blade. Given:ρ_(ref)(y)=ρ(y−x _(shift)),   (Eqn. 1),where ρ_(ref)(y) is the reference blade image and ρ(y) is the bladeimage. Then the inner product of the blade image with translates of thereference blade image achieves its maximum at x_(shift), as definedbelow: $\begin{matrix}\begin{matrix}{{\max\limits_{\quad{\Delta\quad x}}{\int{{\rho(y)}{{conj}\left( {\rho_{\quad{ref}}\left( {y + {\Delta\quad x}} \right)} \right)}{\mathbb{d}y}}}} = {\int{{\rho(y)}{{conj}\left( {\rho_{ref}\left( {y + x_{shift}} \right)} \right)}{\mathbb{d}y}}}} \\{= {{\rho }_{L^{2}}^{2}.}}\end{matrix} & \left( {{Eqn}.\quad 2} \right)\end{matrix}$An estimate of x_(shift) is determined in the Fourier domain by:∫ρ(y)conj(ρ_(ref)(y+Δx))dy=[{circumflex over (ρ)}conj({circumflex over(ρ)}_(ref))]^(v)(Δx)  (Eqn. 3),where {circumflex over (ρ)} denotes the Fourier transform and ρ^(v) isthe inverse Fourier transform.

For datasets with ρ(x)=ρ_(ref)(x−x_(shift)+n(x) where n is Gaussiannoise yield the standard convolution of a blade, ρ, with ρ_(ref) isclose to the L² norm of the “true” noise-free convolution. For purposesof determining the appropriate parameters for a motion correctionalgorithm, the point x_(shift), rather than the convolution functionitself, is desired. What can be problematic, however, is that theconvolution function is generally very smooth and, as a result, themaximum point is not well-defined. This is illustrated in FIG. 4. Asshown, the magnitude of the convolution 87 has a unique maximum point89, but is difficult to localize on a low-frequency discrete lattice.Zero-padding k-space blades increases resolution of the finalconvolution, further reducing the difficulty of localizing the peaksignal.

Accordingly, the present invention is directed to high-pass filtering ofthe convolution of a k-space blade image with a k-space reference bladeimage to determine subject motion (translational and/or rotationalshift) during acquisition of the data for the k-space blade image. Aswill be described, this high-pass filtering will be repeated for eachk-space blade image that is acquired to determine the relative shift ofeach k-space blade image. The k-space reference blade image, in oneembodiment, is generated from the average of all k-space blade images ofa given k-space. However, it is contemplated that the k-space referenceblade images may be determined from the k-space blades of one or morescout scans. Additionally, it is recognized the k-space blade imageacquired immediately before or after a given k-space blade image may beused as the k-space reference blade image for the given k-space bladeimage.

A post-acquisition processing technique to determine subject motionduring data acquisition in accordance with the present invention willnow be described with respect to FIGS. 5-7. Referring now to FIG. 5, thedata of a given k-space blade (for instance, k-space blade 82 of FIG. 3)is shown measured on a Cartesian grid rotated by the acquisition bladeangle schematically represented as “dots” 90. The k-space data 90 of theCartesian grid is then transformed onto the Cartesian lattice of thefirst blade acquired, generally referenced as “stars” 91. This is doneso that the center of each k-space blade is sampled at exactly the samepoints in k-space. In another embodiment, the k-space data 90 istransformed onto the polar lattice 92 of FIG. 6 using one of a number ofknown transformation techniques. More particularly, the k-space data 93of the polar lattice 92 and/or Cartesian lattice 91 is evaluated using aSlow Fourier Transform or other algorithm, such as a standard griddingtechnique. A convolution of the blade image rotated by the bladerotation angle and the reference blade image is then determined toestimate in-plane translation. Similarly, the 1D convolution of theFourier transform with respect to the polar angle of data on the polarlattice 92 is convolved with the 1D Fourier transform of the referenceblade's polar data.

The convolution is a high-pass convolution. For purposes of thisinvention, the upper half of the frequency band comprises the highfrequency components. In this regard, the maximum magnitude point of theconvolution, $\begin{matrix}{{{\max\left\lbrack \frac{\hat{{\rho\quad{{conj}\left( {\hat{\rho}}_{ref} \right)}}\quad}}{{{\hat{\rho}{{conj}\left( {\hat{\rho}}_{ref} \right)}}}^{\alpha}} \right\rbrack}\bigvee(x)},{{{{Eqn}.\quad 4}\quad{is}\quad{achieved}\quad{at}\quad x} = {{x_{shift}\quad{for}\quad 0} \leq {\alpha\quad a\quad{real}\quad{{parameter}.}}}}} & \quad\end{matrix}$

In terms of amplitude and phase, Eqn. 4 can be expressed as:$\begin{matrix}{{{\hat{\rho}(k)} = {{A(k)}{\mathbb{e}}^{{\mathbb{i}\phi}{(k)}}}},} & \left( {{Eqn}.\quad 5} \right) \\{{{{\hat{\rho}}_{ref}(k)} = {{A_{ref}(k)}{\mathbb{e}}^{{\mathbb{i}\phi}_{ref}{(k)}}}},} & \left( {{Eqn}.\quad 6} \right) \\{{{{\max\left\lbrack \frac{\hat{{\rho\quad{{conj}\left( {\hat{\rho}}_{ref} \right)}}\quad}}{\hat{\rho}{{conj}\left( {\hat{\rho}}_{ref} \right)}^{\alpha}} \right\rbrack}(x)} = {{\max\left\lbrack {\left\lbrack {AA}_{ref} \right\rbrack^{1 - \alpha}{\mathbb{e}}^{{\mathbb{i}}{({\phi - \phi_{ref}})}}} \right\rbrack}^{\bigvee}(x)}},} & \left( {{Eqn}.\quad 7} \right)\end{matrix}$where:{circumflex over (ρ)}(k), {circumflex over (ρ)}_(ref) (k) are k-spacedata of the blade and reference blade,A(k), A_(ref) (k) are real valued amplitudes of blade and referencedata, andφ(k), φ_(ref) (k) are the phase of the blade and reference blade data inradians.

Assuming that the k-space data is noise-free and with only a shiftbetween ρ and ρ_(ref), and setting α=1.0, then the high-pass convolutionresults in a delta function with a well-defined peak 94, as shown inFIG. 7. That is, setting α=1.0, the convolution of the k-space bladewith the k-space reference blade is effectively high-pass filtered toresult in the δ function illustrated in FIG. 7 with well-defined peak94. In this regard, non-maximum magnitude data 96 is effectively quashedthereby making peak 94 conspicuous and easily identifiable. Asreferenced above, the position rather than the magnitude of the peak isused to determine a shift in the k-space blade relative to the k-spacereference blade that is typically the result of subject motion duringacquisition of the k-space blade. The δ function may be defined by:$\begin{matrix}{{\delta\left( {x - x_{shift}} \right)} = {\left\lbrack \frac{\hat{{\rho\quad{{conj}\left( {\hat{\rho}{ref}} \right)}}\quad}}{{\hat{\rho}{{conj}\left( {\hat{\rho}{ref}} \right)}}} \right\rbrack^{\bigvee}{(x).}}} & \left( {{Eqn}.\quad 8} \right)\end{matrix}$

Once the point of shift is identified and localized, an appropriatemotion correction algorithm can be identified and implemented inaccordance with known motion correction techniques.

While an exemplary value of α=1.0 has been described, it is understoodthat other values may be used. For example, testing suggests that α=½yields a well-defined peak that can be quickly identified. Moreover, itis preferred that α≧0. Also, an exemplary value of α=1.0 was used fornoise-free data; however, it is recognized that other values may bepreferred for MR data having noise.

Additionally, while the high-pass filter defined by Eqn. 4 is preferred,it understood that other high-pass filters may be used. For example, thehigh-pass filter may be defined by the following expression:max[{circumflex over (ρ)}(k)conj({circumflex over (ρ)}_(ref)(k))|k|^(β)]^(v)(x)=x _(shift) for β≧0  (Eqn. 9).

The present invention has been described with respect to determiningmotion in a subject during acquisition of a k-space blade usingPROPELLER. It is understood, however, that the present invention mayalso used in PROPELLER-variant acquisitions, such as split-bladePROPELLER and TURBOPROP, as well as equivalents thereof. Additionally,the present invention can be used to effectively identify and localizesubject motion embodied as translational shift and/or rotational shift.In this regard, the present invention can be carried out with 1D as wellas 2D convolutions. Accordingly, the present invention improves imagequality by providing more accurate estimates of rotation and/or shift.

Therefore, in accordance with one embodiment of the invention, an MRsystem includes a plurality of gradient coils positioned about a bore ofa magnet to impress a polarizing magnetic field. An RF transceiversystem and an RF switch are controlled by a pulse module to transmit andreceive RF signals to and from an RF coil assembly to acquire MR images.The MR system also includes a computer programmed to acquire a pluralityof k-space blades from a subject in motion during data acquisition, eachk-space blade rotated about a center of k-space. The computer is furtherprogrammed to determine a k-space reference blade and determine ahigh-pass convolution of a k-space blade image with the referencek-space blade image. The computer then determines, from the high-passconvolution, motion of the subject during acquisition of the k-spaceblade relative to the k-space reference blade.

In accordance with another embodiment of the present invention, the MRsystem includes a plurality of gradient coils positioned about a bore ofa magnet to impress a polarizing magnetic field and an RF transceiversystem and an RF switch controlled by a pulse module to transmit RFsignals to an RF coil assembly to acquire MR images. The system furtherhas a computer programmed to acquire a plurality of k-space blades froma subject in motion during data acquisition, each k-space blade rotatedabout a center of k-space. The computer is further programmed todetermine a k-space reference blade image and convert k-space data froma given k-space blade as well as a k-space reference blade to a commonpolar lattice. The computer is further programmed to Fourier transformthe given k-space blade and the k-space referenced blade and determine ahigh-pass convolution of the Fourier transforms with respect to polarangle of the k-space reference blade and the given k-space blade. Fromthe high-pass convolution, the computer is further programmed todetermine in-plane rotation of the subject during acquisition of thek-space blade relative to the k-space reference blade.

According to another embodiment, the present invention is directed to amethod of MR imaging whereby a k-space blade extending through a centerof k-space from a subject in motion is acquired. A high-pass convolutionof the k-space blade with a reference k-space blade is then determinedand converted to a δ function. In-plane motion of the subject duringdata acquisition of the k-space is then determined from the δ function.

In accordance with another embodiment, the invention is embodied in acomputer program stored on a computer readable storage medium and havinginstructions which, when executed by a computer, cause the computer toacquire a k-space blade extending through an origin of k-space from asubject in motion during data acquisition. The computer is furthercaused to represent the k-space blade on a rotated lattice and determinea convolution of the k-space blade with a reference k-space blade. Thecomputer is further programmed to high-pass filter the convolution anddetermine at least one of a rotational or a transitional shift of thesubject during acquisition of the k-space blade relative to thereference k-space blade.

The present invention has been described in terms of the preferredembodiment, and it is recognized that equivalents, alternatives, andmodifications, aside from those expressly stated, are possible andwithin the scope of the appending claims.

1. A magnetic resonance (MR) system comprising: a plurality of gradientcoils positioned about a bore of a magnet and configured to impress apolarizing magnetic field; an RF transceiver system having an RF switchand controlled by a pulse module to transmit RF signals to an RF coilassembly to acquire MR data; and a computer programmed to: acquire atleast one blade of MR data from a subject; define a reference blade;reconstruct the at least one blade of MR data and the reference bladeinto at least one blade image and a reference blade image, respectively;perform a high-pass convolution of the at least one blade image with thereference blade image; and determine a motion of the subject duringacquisition of the at least one blade of MR data therefrom.
 2. The MRsystem of claim 1 wherein the high-pass convolution includes a twodimensional convolution.
 3. The MR system of claim 2 wherein thecomputer is further programmed to determine the motion of the subject asan in-plane subject translation using the two dimensional convolution.4. The MR system of claim 1 wherein the high-pass convolution includes aone dimensional convolution.
 5. The MR system of claim 4 wherein thecomputer is further programmed to determine the motion of the subject asa subject rotation using the one dimensional convolution.
 6. The MRsystem of claim 1 wherein the computer is further programmed to performthe high-pass convolution by, in part, dividing a convolution functionof the at least one blade image and the reference blade image by a powerof the convolution function.
 7. The MR system of claim 1 wherein thecomputer is further programmed to determine a delta function from thehigh-pass convolution.
 8. The MR system of claim 7 wherein the computeris further programmed to determine a maximum value of the delta functionto determine the motion of the subject.
 9. A method for subject motiondetermination in an MR imaging procedure comprising: determining anumber of segments of MR data rotated about a center of k-space;computing a reference segment of MR data; transforming the referencesegment of MR data and the number of segments of MR data into areference segment of image data and a number of segments of image data,respectively; determining a convolution function for each of the numberof segments of image data with the reference segment of image data;accentuating a peak of each convolution function; and identifying pointsat which each convolution function achieves a maximum value.
 10. Themethod of claim 9 wherein computing the reference segment of MR dataincludes one of averaging the number of segments of MR data, averagingMR data acquired in a scout scan, or setting the reference segment of MRdata for a given one of the number of segments of MR data as apreviously acquired segment of MR data of the number of segments of MRdata.
 11. The method of claim 9 wherein accentuating a peak of eachconvolution function includes at least one of high-pass filtering eachconvolution function and determining a delta function for eachconvolution function.
 12. The method of claim 11 comprising dividingeach given convolution function by a power of the given convolutionfunction.
 13. The method of claim 11 comprising multiplying theconvolution function by a power of a magnitude of a Fourier variable ofthe number of segments of image data and the reference segment of imagedata.
 14. The method of claim 9 wherein transforming the referencesegment of MR data and the number of segments of MR data and determiningthe convolution function for each of the number of segments of MR datawith the reference segment of MR data include Fourier upsampling thenumber of segments of MR data the zero-padding each of the number ofsegments of MR data.
 15. A data storage medium having a set ofinstructions stored thereon which, when executed by a processor, causesthe processor to: perform a transformation of at least one blade of MRdata and a reference blade into at least one set of MR image data and areference set of image data, respectively; determine a convolution ofthe transformation of the at least one blade of MR data and thereference blade high-pass filter the convolution to determine a subjectshift during acquisition of the at least one blade of MR data relativeto the reference blade; and apply a motion correction algorithm based onthe subject shift.
 16. The data storage medium of claim 15 wherein theset of instructions further causes the processor to high-pass filter theconvolution by one of dividing the convolution by a power of thetransformation or multiplying the convolution by a power of a magnitudeof a Fourier variable of the transformation.
 17. The data storage mediumof claim 15 wherein at least one of the transformation and theconvolution include Fourier upsampling the at least one blade of MR dataand zero-padding the at least one blade of MR data.
 18. The data storagemedium of claim 15 wherein the instructions further cause the processorto determine a convolution function having attenuated non-maximum datafrom high-pass filtering the convolution.
 19. The data storage medium ofclaim 15 wherein the instructions further cause the processor to definethe reference blade as one of an average of a number of blades of MRdata, an average of MR data acquired in a scout scan, or as anotherblade of MR data acquired prior to the at least one blade of MR data.20. The data storage medium of claim 15 wherein the instructions furthercause the processor to determine at least one of a one dimensionalconvolution of the transformation to determine a subject rotation and atwo dimensional convolution of the transformation to determine a subjecttranslation.